For years, interactions between double stranded (duplex) DNA were presumed to be independent of the DNA structure and base pair sequence because the nucleotides are buried inside the double helix and shielded by the highly charged sugar-phosphate backbone. In discussion of such interactions, duplex DNA was explicitly or implicitly modeled as a uniformly charged cylinder. However, this concept was based on intuitive perception rather than experiments or rigorous theory. In reality, the experimental evidence, e.g., transformation of duplex DNA from a non-ideal helix with 10.5 base pairs/turn in solution into a nearly ideal helix with 10.0 bp/turn in aggregates, suggested that this concept may be wrong. Starting from the classical paper of Rhodes and Klug published in 1980, it became clear that interactions between duplex DNA not only depend on but also affect the double helix structure. To account for possible effects of the structure of the sugar phosphate backbone on DNA-DNA interactions, over the last decade we have been developing a theory of electrostatic interactions between macromolecules with helical patterns of surface charges. Even the simplest models, which did not account for dynamic variations in the structure, e.g., due to the thermal motion, already suggested possible explanations for many observations. Such observations included the torsional deformation of the double helix upon aggregation mentioned above, counterion-specificity of DNA condensation, multiple liquid crystalline phases in DNA aggregates, and measured intermolecular forces. We, therefore, continued development of this theory and its applications to various phenomena. Most importantly, this theory predicted that the dependence of the backbone structure on the nucleotide sequence might be sufficiently strong to affect DNA-DNA interactions. The structure-specific DNA-DNA interactions result from preferential juxtaposition of the negatively charged sugar phosphate backbone with counterions bound in grooves on the opposing molecule. Our analysis of x-ray diffraction experiments confirmed such juxtaposition of parallel DNA molecules in fibrous, hydrated aggregates. Furthermore, statistical analysis and comparison of known structures of DNA oligonucleotides in crystals (determined by x-ray diffraction) and in solution (determined by NMR) revealed changes in DNA structure within the crystals consistent with predictions of this theory and allowed us to evaluate essential parameters of the theory. However, it remained unclear how sequence-dependent interactions might be affected by thermal fluctuations, particularly by DNA bending. In the last several years, we developed and published a comprehensive statistical theory, which predicted dramatic effects of thermal bending. Contrary to our expectations, thermal undulations of DNA strongly amplify rather than weaken the sequence-dependent interactions. The undulations enhance the structural adaptation of DNA, leading to better alignment of neighboring molecules and pushing the geometry of the DNA backbone closer to that of an ideal helix. Quantitative comparison revealed good agreement of the theoretical predictions with measured osmotic pressures in DNA aggregates. We utilized these results for refining DNA fiber x-ray diffraction theory. Comparison of the latter theory with available experimental diffraction patterns further supported our predictions for the relationship of the double helix sequence and structure with DNA-DNA interactions. During the last several months, we further extended the theory to account for large thermal rotations of the molecules, which are important in interactions between relatively short (20-80 bp) oligonucleotides, and analyzed several recent experimental studies of oligonucleotides. Our theory appears to explain such puzzling observations as resistance of double-stranded ds-RNA oligonucleotides to condensation by counterions that condense their ds-DNA counterparts and condensation of triple-stranded ts-DNA by alkaline earth metal ions that do not condense ds-DNA. The effects of the sequence on interactions between duplex DNAs, e.g., the predicted direct recognition of sequence homology between 100 base pair (bp) or longer sequences, may have significant biological implications. For instance, the speed and accuracy of sequence homology recognition is crucial for DNA repair, preventing DNA lesions that lead to cell death and cancer. In 2008, we publishedthe first experimental evidence for homologous pairing of 300 bp, intact DNA double helices in liquid crystalline aggregates. These experiments and published reports, which indicated that homologous, nucleosomes-free regions of duplex DNA might preferentially interact in vivo, suggested that local, transient pairing of homologous sequences in intact DNAs may precede double strand breaks, further recognition by protein-covered single strands, and strand crossover. In late 2009, the group of M. Prentiss from Harvard University published elegant single-molecule studies, which revealed selective binding of 1-5 kb duplex DNA fragments to homologous regions on much longer molecules, further supporting our theory. Surprisingly, however, they observed this binding in monovalent salt, at conditions at which pairing or aggregation of duplex DNAs was never observed before and was considered to be theoretically impossible. In our theory, a stable parallel juxtaposition of two homologous DNA duplexes was expected to occur in the presence of some divalent and most polyvalent counterions, but not in monovalent salt. To resolve the potential discrepancy between our predictions and the experimental observations of M. Prentiss group, we revisited the theory of electrostatic pairing between duplex DNA. Specifically, we eliminated the simplifying assumption that DNA duplexes remain straight and parallel to each other when they form a stable pair. We found that DNA molecules will tend to supercoil, forming a braid. In the last several years, we completed and published a theory for the electrostatic energy of such braids, demonstrating that formation of stable braided pairs of homologous double helices may be energetically favorable even in monovalent salt, depending on counterion environment. Our predictions for the dependence of such pairing on counterions, salt concentration and temperature closely matched the experimental observations of the Prentiss group. Furthermore, this theory suggested possible interpretation for a number of other puzzling phenomena. For instance, electrostatic stabilization of left-handed braids predicted by this theory may be an important factor in explaining why hyperthermophilic bacteria and archea need reverse gyrases to promote left-handed supercoiling of circular DNA, which provides more stable conformation (essential for protecting the genome at temperatures above 100 C). Experiments designed to test some of these ideas are currently in progress in several laboratories, including the laboratory of our collaborators at the Imperial College London.